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lfunc_lfunctions • Show schema
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{'Lhash': '3882630400872917762933545242198', 'a10': [0.0, 0.0], 'a2': [1.3449970239279148, -1.3449970239279148], 'a3': [0.1786713462201903, -0.43135078725224224], 'a4': [0.0, -2.618033988749895], 'a5': [0.0, 0.0], 'a6': [-0.3398530961958789, -0.8204779540505789], 'a7': [-1.4050470160347004, 0.5819895298134204], 'a8': [-2.1762508994828216, -2.1762508994828216], 'a9': [0.5529667294835535, 0.5529667294835535], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.39875294509376896, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [-0.8090169943749475, 0.5877852522924731]]], [47, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [17, 47], 'central_character': '799.93', 'coefficient_field': 'CDF', 'conductor': 799, 'conductor_radical': 799, 'conjugate': '1892091727389863332403255388227', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3449970239279148, 1.3449970239279148], [0, -1.0]], [[1.0, 0], [-0.1786713462201903, 0.43135078725224224], 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'root_analytic_conductor': 0.6314688789590259, 'root_angle': 0.7758214859008884, 'root_number': '-0.76207951012266720527234092272276 + 0.64748345171996139025071266216475*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3879107429504442', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.06285533267122985110171892950', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.71907855731235172943011023353', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.44843438381123805269516216009', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.39875294509376896, 'bad_primes': [17, 47], 'central_character': '799.93', 'conductor': 799, 'conductor_radical': 799, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/799/1/h/b/93/4'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-799-799.93-c0-0-4', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-799-799.93-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6314688789590259, 'root_angle': 0.3879107429504442, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.06285533267122985110171892950', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3882630400872917762933545242198', 'Lhash_array': ['3882630400872917762933545242198'], 'label': '2-799-799.93-c0-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/799/1/h/b/93/4'}